Boundedness of operators of Hardy type in ΛP,q spaces and weighted mixed inequalities for singular integral operators

We consider certain n -dimensional operators of Hardy type and we study their boundedness in These spaces were introduced by M. J. Carro and J. Soria and include weighted L p, q spaces and classical Lorentz spaces. As an application, we obtain mixed weak-type inequalities for Calderón—Zygmund singular integrals, improving results due to K. Andersen and B. Muckenhoupt.